MAXIMUM POWER TRANSFER

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HISTORY

Moritz Hermann von Jacobi

1840s – published the Maximum Power Theorem also known as Jacobi’s Law.

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MAXIMUM POWER TRANSFER THEOREM:

“Maximum power is transferred when the internal resistance of the source equals the resistance of the load, when the external resistance can be varied, and the internal resistance is constant.”

Jacobi

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THE THEOREM…

Aims : to transfer maximum power to the load

Important : for safety purposes.

Helps : maintain over-all efficiency high.

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RECALL: MPT AT DC CIRCUITS

FIXED RESISTANCE

VARIABLE

RESISTANCE

@MPT: R=RL

RESTATING, when fixed internal resistance of source is equal to the value of variable external (load resistance) , maximum power transfer is achieved.

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P 8MPT

AT AC CIRCUITS

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THEOREM TO AC CIRCUITS:

Maximum power transfer occurs when the load impedance is equal to the complex conjugate of the source impedance.

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MAXIMUM POWER TRANSFER WITH AC CIRCUITS HAS THREE CASES…

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CASE 1:

LOAD : VARIABLE RESISTANCE

ZL

ZG

@MPT: ZL=RL=ZG

When load is purely resistive and adjustable, maximum power transfer is achieved. When…

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Problem: In the circuit of the figure shown, the load ZL

consists of a pure resistance RL. Find the value of RL for which the source delivers maximum power to the load. Determine the value of PMAX.

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CASE 2:

LOAD : VARIABLE RESISTANCE

AND VARIABLE INDUCTIVE REACTANCE

ZG

@MPT: XL=-XG

RL =RG

ZL

When RL and XL are both independently adjustable, MPT is achieved when XL = -XG and RL = RG.

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Problem:

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CASE 3:

LOAD : VARIABLE RESISTANCE AND FIXED INDUCTANCE

ZG

@MPT:

ZL

When XL is fixed and RL is adjustable, MPT is achieved when

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Problem:

In the network shown, the load connected across terminals AB consists of a variable resistance RL and a capacitive reactance of XC which is variable between 2 and 8 ohms. Determine the values of RL and XC which results in maximum power transfer. Calculate the maximum power P delivered to the load.

 

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SUMMARY:

When load is purely resistive and adjustable, MPT is achieved when

When RL and XL are both independently adjustable, MPT is achieved when XL = -XG and RL = RG.

When XL is fixed and RL is adjustable, MPT is achieved when

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REFERENCES:

Books:

Electrical Circuits

Charles S. Siskind

Fundamentals of Electric Circuits

Alexander & Sadiku

Websites:

Electronics Tutorials

http://www.electronics-tutorials.ws/dccircuits/dcp_9.html

All About Circuits

http://www.allaboutcircuits.com/vol_1/chpt_10/12.html

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MEMBERS:

GARINGLATIZA NAGUITRODRIGUEZVILLEGAS